Alright, let's solve this problem step by step. We have 9257 and 8632 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 2 in column 1 and get 9.

Step 2: We'll start by adding the digits 5 & 3 in column 2 and get 8.

Step 3: We'll start by adding the digits 2 & 6 in column 3 and get 8.

Step 4: We'll start by adding the digits 9 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 9257 + 8632 = 17889.

